Chapter 1.1, Problem 53E

To determine

To find the Area of the base $B$ of the solid −

  

Answer to Problem 53E

The Base Area is $12\pi$$i{n}^2$ .

Explanation of Solution

Given:

  

Height of the cylinder - $h=7$$in$ .

Volume of the cylinder - $V=84\pi$$i{n}^3$ .

Formula Used:

Volume of the cylinder $=$ Base Area $\times$ Height

Calculation:

Given:

Height of the cylinder - $h=7$$in$ .

Volume of the cylinder - $V=84\pi$$i{n}^3$ .

As per the given formula, we have:

Volume of the cylinder $=$ Base Area $\times$ Height

  $84\pi =B\times 7$

Solving the above equation, we have:

  $\begin{array}{l}84\pi =B\times 7\\ B=\frac{84\pi }{7}\\ B=12\pi \end{array}$

Thus, the Base Area is $12\pi$$i{n}^2$ .

Conclusion:

Hence, the Base Area is $12\pi$$i{n}^2$ .